第二类抛物型变分不等式中的MRM方法

本文讨论了第二类抛物型变分不等式中的MRM(多重互易方法)方法。首先采用时间项半离散和隐格式方法将抛物型变分不等式化解为一个椭圆变分不等式，然后利用MRM-边界积分方程，将其化解为MRM-边界混合变分不等式，并给出了MRM-边界混合变分不等式解的存在唯一性。说明了该MRM-边界混合变分不等式与常规边界积分方程得到的边界混合变分不等式是一致的，并且具有更容易编程实现。这为使用MRM边界元方法数值求解抛物型变分不等式提供了方法和理论依据。文末给出了数值算例。

Multiple Reciprocity Method for Parabolic Variational Inequalities of Second Kind

The multiple reciprocity method (MRM) for the parabolic variational inequalities of the second kind was discussed. First, the parabolic variational inequalities can be transformed into an elliptic variational inequality by using semi-discretization and implicit method in time; then using the MRM-boundary integration equation, the MRM-boundary mixed variational inequality was construct, and the existence and uniqueness of the corresponding variational inequality of second kind were given. It shows that the MRM-boundary mixed variational inequality is in accordant with the one derived by traditional boundary mixed variational inequality and it also demonstrates that it has the additional advantage of easy programming. These works provide the theoretical basis for using MRM boundary element method to solve the mixed parabolic variational inequality. Finally the numerical example was given.